All about the numbers

When a particular subject lights something up inside you, it’s worth taking notice. For me, one of those is the numbers – specifically the whole numbers, or integers. Thus was I from childhood drawn to mathematics, and later to Greek philosophy via Pythagoras. The former gave the outer mechanics of numbers, the latter suggested that numbers had a more mystical and imprecise meaning, leading to later interests in subjects such as numerology, and to astrology, where the numbers lurk in the background.

So I was a sucker for these two books which approach the numbers in completely different ways:

  • Music by the Numbers by Eli Maor
  • The Archetype of Number and its Reflections in Contemporary Cosmology, by Alain Negre

music by the numbersFor people such as me, Eli Maor has written an engaging book about the relationship between music and mathematics. The development of musical scales from Pythagoras to the early 20th century is an interesting story, reasonably well explained, from Pythagoras’s whole number ratios through the equal tempered scale exemplified in the work of JS Bach to the experiments of Stravinsky and Schoenberg.

The fascination still seems to lie in those magical simple ratios of musical resonance: the octave 2:1, the fifth 3:2 and the fourth 4:3, from which are derived the Pythagorean Scale, which is nearly ‘right’, but in the end not adequate for use in orchestras with different sort of instruments, as Maor explains. Always the whole numbers are beautifully simple, but prove too limited to describe the real world, hence the subsequent invention of all the panoply of mathematics, irrational numbers, imaginary numbers, the calculus and on and on.

And in the end, always and tantalisingly, the maths cannot fully describe the real world, which we know thanks to the insights of Kurt Gödel.

archetype of the numberAlain Negre’s book is about number as archetype – the qualitative aspect of number, which was revived in the 20th century by psychologist Carl Jung and physicist Wolfgang Pauli. All begins with 1,2,3, and 4 – just as with the Pythagorean scale. The qualities of these 4 basic numbers are explored and particularly related to the work of Jung, and to the triplicities and quadruplicities of astrology.

There are rather incomprehensible (to me) chapters relating the numbers 3 and 4 to current theories on the evolution of the cosmos – rather speculative, I think. Negre goes on to suggest that the astrological zodiac with the 12 signs is another projection of these number archetypes, including discussion of the axis crosses and the oppositional polarities in a chart of the 12 signs.

So the book is both familiar to me, in an astrological sense, and almost incomprehensible when relating to modern cosmology, which must be partly due to my own failure to keep up with this field. In fact, I had a similar reaction to an earlier work some years ago Number and Time by Marie-Louise von Franz. It feels like there is something important there, but the author has not quite managed to express it in a way that is easily comprehensible to me (of course this may be a commentary on me, rather than on the author’s work).

So yes, number still has that magical pull, but these books didn’t greatly enlightened me. Nor did they blunt that fascination with the numbers.

Music by the Numbers is much the more readable.

Everybody Knows

The first two verses of Leonard Cohen’s lyrics in the track ‘Everybody Knows’ seem an apposite comment on the recent UK General Election.

Everybody knows that the dice are loaded
Everybody rolls with their fingers crossed
Everybody knows that the war is over
Everybody knows the good guys lost
Everybody knows the fight was fixed
The poor stay poor, the rich get rich
That’s how it goes
Everybody knows

Everybody knows that the boat is leaking
Everybody knows that the captain lied
Everybody got this broken feeling
Like their father or their dog just died
Everybody talking to their pockets
Everybody wants a box of chocolates
And a long stem rose
Everybody knows

Here’s the rest, or listen here.

Everybody knows that you love me baby
Everybody knows that you really do
Everybody knows that you’ve been faithful
Ah give or take a night or two
Everybody knows you’ve been discreet
But there were so many people you just had to meet
Without your clothes
And everybody knows

And everybody knows that it’s now or never
Everybody knows that it’s me or you
And everybody knows that you live forever
Ah when you’ve done a line or two
Everybody knows the deal is rotten
Old Black Joe’s still pickin’ cotton
For your ribbons and bows
And everybody knows

And everybody knows that the Plague is coming
Everybody knows that it’s moving fast
Everybody knows that the naked man and woman
Are just a shining artifact of the past
Everybody knows the scene is dead
But there’s gonna be a meter on your bed
That will disclose
What everybody knows

And everybody knows that you’re in trouble
Everybody knows what you’ve been through
From the bloody cross on top of Calvary
To the beach of Malibu
Everybody knows it’s coming apart
Take one last look at this Sacred Heart
Before it blows
And everybody knows

Everybody knows, everybody knows
That’s how it goes
Everybody knows

Way down yonder in New Orleans

There’s just something special about New Orleans and that jazzy/bluesy French Quarter with its Spanish colonial architecture. So unlike most of the US!

Eyes in the back of my Head

New Orleans – NOLA – has its own very special vibrant energy and appeal. I went there recently for a short break, took my camera and tried to capture some of the many aspects of this incredible city.

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 The jazz band in the square outside the cathedral clearly paid no attention to the sign on the lamp post.

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The Natchez steams away from the dockside, hooting and churning up the Mississippi mud on a damp Sunday morning.

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For Mardi Gras, the previous week, even the carriage horse’s hooves were decorated.

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A hot dog vendor trundles to work through a quiet road in the French Quarter.

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Cool saxophone jazz on a street corner.

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The sign says “I wonder what happens if you put $$ in the box”. The statue moved and gave the donor a card with a short, positive sentence written on it.

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Lively street parades happen often.

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Outside a…

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Everybody knows

Everybody knows that the dice are loaded
Everybody rolls with their fingers crossed
Everybody knows that the war is over
Everybody knows the good guys lost
Everybody knows the fight was fixed
The poor stay poor, the rich get rich
That’s how it goes
Everybody knows

Everybody knows that the boat is leaking
Everybody knows that the captain lied
Everybody got this broken feeling
Like their father or their dog just died

Everybody talking to their pockets
Everybody wants a box of chocolates
And a long stem rose
Everybody knows…

So much in the words of a song, by Leonard Cohen.

Listen to it on YouTube.

Pic by Rama via Wikimedia Commons.